Mathematical Sciences: Non-Locally Convex Spaces and Their Applications in Analysis

数学科学：非局部凸空间及其在分析中的应用

• 批准号: 8901636
• 负责人: Nigel Kalton
• 金额: $ 16.22万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-05-01 至 1993-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901636&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Non; Locally; Convex

Professor Kalton's research project continues his investigation of mathematical objects encountered at a fairly high level of abstraction in analysis. At the most concrete level of this subject, one is concerned with summing series, integrating functions, solving differential equations, and the like. Moving up a notch in generality, it has been found to be advantageous to amalgamate the analytic objects one is dealing with into what are called Banach spaces (in the most favorable situations) or other sorts of linear spaces. These spaces in turn can be studied either individually, or along the lines of a general theory. The present project deals with spaces that are related to Banach spaces but do not fit strictly within that category. There is for instance a construction called the twisted sum that is most naturally viewed in a much larger category of functional analytic objects than that of Banach spaces. Two of the latter can have a twisted sum that is not even locally convex. Kalton will study decomposition and extension properties defined with respect to twisted sum, and the connections of this notion with interpolation theory. His methods are expected to have repercussions for problems usually approached just from within the Banach space context.

卡尔顿教授的研究项目继续着他的 调查数学对象遇到了一个公平的 分析中的高度抽象。在最具体的层面上 在这门学科中，一个是关于级数求和的， 积分函数，解微分方程， 如.在一般性上，已经发现 有利于分析对象的融合 与到什么是所谓的巴拿赫空间（在最有利的 或者其他类型的线性空间。这些空间反过来 可以单独研究，也可以沿着 一般理论本项目涉及的空间， 与Banach空间有关，但并不严格符合 类别. 例如，有一种结构称为扭曲和 这是最自然地在更大的类别中看待的 比Banach空间的函数分析对象。两 后者可以具有甚至不是局部的扭曲和 凸的Kalton将研究分解和扩展特性 关于扭曲和定义，以及这个的连接 内插理论的概念。他的方法有望 对通常只从 在Banach空间中。